Any proc skill will not interrupt your Cascade > Fountain combo. So you can do, provided you have the procs, Cascade > Fountain > Reverse Cascade > Fountainfall or Cascade > Reverse Cascade > Fountain > Fountainfall. Again provided you have the right procs up. It's the same for the AoE combos as well.

Fan Dance 1 and 2 consume Feathers. You only need one feather to use Fan Dance 1 or 2. Those can trigger Fan Dance 3 but you can't store charges for them like you can 1 and 2 so you want to use that before you use more Fan Dance 1 and 2 skills.